I have to disagree about the use of caulk for a toilet installation over ceramic tile. On a vinyl floor installation this is fine because the floor is relatively smooth. Tile floors, however, may vary in height from tile to tile. Also caulk tends to hide faulty flange seal leaks and becomes discolored rapidly. In any case a toilet should not flex or give at all.
Shimming a toilet is a poor fix for a rocking toilet as the shims may act as a pivot point and crack the toilet. Plumbers putty under the base will provide for a much softer fix. Good flange bolts, properly tightened, are needed as well.
I have had more than a few plumbers bum some grout from me to finish a toilet install off. Besides for the reasons listed above it makes the job look better and no it will not pop out if grouted correctly.